Random Gaussian cubic surface Seed: 145 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.437 x*z^2 +0.0594 y*z^2 -0.647 z^2 -0.229 x^2*z -0.0273 x*y*z -0.151 x*z +0.0377 y^2*z +0.0483 y*z -0.0622 z +0.0786 x^3 +0.196 x^2*y -0.289 x^2 -0.172 x*y^2 -0.0236 x*y -0.00075 x +0.0104 y^3 +0.0112 y^2 -0.276 y -0.262 1
Affine cubic: f(x,y,z) = -0.437 x*z^2 +0.0594 y*z^2 -0.647 z^2 -0.229 x^2*z -0.0273 x*y*z -0.151 x*z +0.0377 y^2*z +0.0483 y*z -0.0622 z +0.0786 x^3 +0.196 x^2*y -0.289 x^2 -0.172 x*y^2 -0.0236 x*y -0.00075 x +0.0104 y^3 +0.0112 y^2 -0.276 y -0.262 1
Shadow: the quartic B(x,y)^2 - 4 A(x,y) C(x,y) = 0 is drawn on the z=-4 xy-plane in the same 3D scene. The translucent ruled curtain rises upward from the shadow to the ramification curve where the lifted point has z >= -2 and lies above the displayed projection plane. The 3 real projected lines on the xy-plane are bitangents found from the projective lines on the cubic surface. Same-color transparent line projection cones are included but hidden by default; use the page toggle to show them.
Viewing box: axis ranges are [-4, 4].